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Algebra i logika, 2018, Volume 57, Number 3, Pages 362–376
DOI: https://doi.org/10.17377/alglog.2018.57.307 (Mi al854) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators

M. P. Shushpanov

El'tsyn Ural Federal University, ul. Mira 19, Yekaterinburg, 620002 Russia
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DOI: https://doi.org/10.17377/alglog.2018.57.307
Abstract: It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.
Keywords: left-modular element, right-modular element, seminormal element, defining relation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Supported through the Competitiveness Project (Agreement No. 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University).
Received: 25.11.2016
Revised: 23.02.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 3, Pages 237–247
DOI: https://doi.org/10.1007/s10469-018-9496-3
Bibliographic databases:
Document Type: Article
UDC: 512.565
Language: Russian
Citation: M. P. Shushpanov, “Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators”, Algebra Logika, 57:3 (2018), 362–376; Algebra and Logic, 57:3 (2018), 237–247
Citation in format AMSBIB
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\paper Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators
\jour Algebra Logika
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\vol 57
\issue 3
\pages 362--376
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\jour Algebra and Logic
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
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